Solving Systems of Linear Equations: Linear Combinations — Quiz
Question 6 • Algebra I
To eliminate the x -terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: 6 x minus 5 y is equal to 17 Second equation: 7 x plus 3 y is equal to 11
Answer
A
The first equation should be multiplied by 7 and the second equation by negative 6 .
B
The first equation should be multiplied by 7 and the second equation by 6 .
C
The first equation should be multiplied by 3 and the second equation by negative 5 .
D
The first equation should be multiplied by 3 and the second equation by 5 .
Explanation
To eliminate x by adding, make the x-coefficients opposites. Multiplying the first equation by 7 gives 42x, and multiplying the second by −6 gives −42x. These terms cancel when the equations are added, so the correct choice is the first equation by 7 and the second by −6.
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